Gröbner bases, Gaussian elimination and resolution of systems of algebraic equations. (English) Zbl 0539.13002

Lazard, D.

Computer algebra, EUROCAL ’83, Proc. Conf., London 1983, Lect. Notes Comput. Sci. 162, 146-156 (1983).

[For the entire collection see Zbl 0532.00010.]
The relationship between different methods for solving systems of algebraic equations are considered. - Using the algebraic geometry approach upper and lower bounds for the degrees of the elements of a Gröbner base are given. It is shown that these degrees depend on the choice of ordering. The extremal cases are lexicographical orderings leading to Gröbner bases of high degree and reverse lexicographical orderings giving low degrees.

Reviewer: K.Peeva

MSC:

13-04	Software, source code, etc. for problems pertaining to commutative algebra
13F20	Polynomial rings and ideals; rings of integer-valued polynomials
65H10	Numerical computation of solutions to systems of equations
13A15	Ideals and multiplicative ideal theory in commutative rings
12E12	Equations in general fields
14A05	Relevant commutative algebra
68Q25	Analysis of algorithms and problem complexity

Keywords:

Gaussian elimination; systems of algebraic equations; Gröbner base